To get Season currency when your hero's or team's ranking resets, you need to play at least 3 fights during the Season with this hero/team. You have to play 3 fights specifically in ranking fights.
Season currency is awarded for reaching ranking thresholds—milestones. Detailed information about rewards and the ranges of rankings can be found inside the game itself. In the in-game Hero Library, there are full descriptions of the ranking thresholds, with threshold designations, and the reward for each milestone.
After the rankings are reset and 3 fights have been played in the new season, you receive currency for each milestone reached in the current ranking of your hero or team.

You can spend Season currencies on purchases in the relevant section of the store. Season currency can only be obtained in Seasons. You cannot buy Season currency or earn it in other game activities. The content of the Season store changes every month.